Absorption of light is done by means of pigment. All predominant pigments absorb in violet-blue region (400nm-470nm), whereas only chlorophyll and phytochrome absorb in red (645nm-750nm). Plant response to light is complex and results from a combination of biological processes induced by pigmentsd absorption. The perfect red:blue ratio depends on the quantities of pigments inside the plant and on the effect you want to induce : germination, flowering, fruiting... The ratio red:far red is also a parameter which may influence the behavior of the plant (photoperiodism).
As far as I know, it is easier to accurately control the light (spectrum, intensity) than to observe or predict the behavior on a plant. But I am really interested to know if there are more direct method for that.
If I comprehend correctly, we should be able to predict an ideal red:blue ratio if we know the ratio of various pigments in my cell?
I am keen on studying my cell's growth performance under an "optimum ratio of red:blue" and hence variation in intensity is not a criteria I am considering at the moment.
When you say "cell's growth performance," it implies you are culturing cells in vitro. Without knowing anything about them, it is impossible to predict how they will respond to a specific spectral power distribution.
As Olivier noted, "plant response to light is complex," in part because plant cells use photopigments to mediate photosynthesis, photomorphogenesis, phototropism, entrainment of circadian and circannual clocks, shade avoidance syndrome, the production of flavonoids, protection against ultraviolet radiation, fungal infections, insect herbivory ... the list goes on.
But more important for your study is the intensity (technically irradiance) of your cells. Even considering photosynthesis alone, any photosynthetic organism will have a limit beyond which the photosynthesis apparatus saturates, and the cells may be damaged. Too little irradiance and the cells may not thrive.
Another point: the use of red (~660 nm) and blue (~450 nm ) in LED-based horticultural luminaires is based solely on the photosynthesis needs of the plants. Plant photopigments , however, have action spectrums ranging from 280 nm (ultraviolet-B, to which UVR8 responds) to 800 nm (far-red, to which the Pfr isoform of phytochrome responds). Healthy plants benefit from radiation throughout this spectral range (with the exception of yellow light, which appears to have an inhibitory effect on the growth of lettuce).
Finally, it is important not to generalize from in vitro to in vivo experiments. As but one example, the absorption spectra of phytochrome isoform Pr is shifted some 30 nm towards green (from 660 nm to 630 nm) by the overwhelming presence of chlorophyll in vivo.
Bottom line: even if you could predict the "ideal" blue-red ratio for optimal cell growth performance (which implies a predefined metric), the results would be specific to a particular in vitro cell cultured under specific conditions.
The reason I mention "cell's growth performance" is because I had microalgal cells in mind while addressing this question (I should have mentioned that earlier). However, I am also keen on understanding plant responses in order to have a fair idea while extrapolating the logic to unicellular species.
From the answers I understand that specie response to spectral ranges is varied and may have to be tested experimentally. It may have to be a trial process wherein different ratios are attempted to find the best combination for high growth rates.
For your experimental plan, I would recommend to take care about the features of the light received by cells, i.e. irradiance, uniformity of irradiance and spectral range. The source and the optical system (which can be simply a black or white cavity for instance) may be designed in accordance to the lighting effect you want to apply. Wavelength dependent reflection and refraction effects may affect the level of energy bring to the cells by photometric errors. Everything can be done using LED and optical chambers, and calculations or accurate photometric measurements will give trust on your experiments results.
Attached a synthetic view about absorption spectrum of main pigments. It may be help.